2,208 research outputs found
Global well-posedness for the micropolar fluid system in the critical Besov spaces
We prove the global well-posedness for the 3-D micropolar fluid system in the
critical Besov spaces by making a suitable transformation to the solutions and
using the Fourier localization method, especially combined with a new
estimate for the Green matrix to the linear system of the transformed equation.
This result allows to construct global solutions for a class of highly
oscillating initial data of Cannone's type. Meanwhile, we analyze the long
behavior of the solutions and get some decay estimates.Comment: 23page
Infinite energy solutions to the homogeneous Boltzmann equation
The goal of this work is to present an approach to the homogeneous Boltzmann
equation for Maxwellian molecules with a physical collision kernel which allows
us to construct unique solutions to the initial value problem in a space of
probability measures defined via the Fourier transform. In that space, the
second moment of a measure is not assumed to be finite, so infinite energy
solutions are not {\it a priori} excluded from our considerations. Moreover, we
study the large time asymptotics of solutions and, in a particular case, we
give an elementary proof of the asymptotic stability of self-similar solutions
obtained by A.V. Bobylev and C. Cercignani [J. Stat. Phys. {\bf 106} (2002),
1039--1071]
The Evaluation of the Efficacy of the R&D European Funds in Piedmont
This paper provides some empirical evidence of the impact of two policy measures, aiming at supporting innovative activity of small and medium firms in Piedmont. Both measures use European Structural Funds, but are managed at a regional level. Measure 2.1b, a concessional loan aiming at stimulating the introduction of innovative plants, machinery and equipments, had positive effects on investments, assets and sales in the short run; but there are hints that investments could have been anticipated from already scheduled projects in the following periods. Measure 2.6b, a free grant aiming at stimulating research activity of firms, had positive effects on intangible investments and capital, but this new knowledge does not seem to be able to directly impact on the production process of the firm. When evaluating the effect for specific groups of firms, for both measures we do not find stronger effects for firms characterized by a high intensity of subsidy. When considering firms with a high cost of capital, we find that Measure 2.1b significantly reduced the interest rate asked by the lenders also after the end of the project, while Measure 2.6b had not been effective at all.
Global well-posedness for the 3D rotating Navier-Stokes equations with highly oscillating initial data
In this paper, we prove the global well-posedness for the 3D rotating
Navier-Stokes equations in the critical functional framework. Especially, this
result allows to construct global solutions for a class of highly oscillating
initial data.Comment: 20page
The Effective Field Theory of Inflation Models with Sharp Features
We describe models of single-field inflation with small and sharp step
features in the potential (and sound speed) of the inflaton field, in the
context of the Effective Field Theory of Inflation. This approach allows us to
study the effects of features in the power-spectrum and in the bispectrum of
curvature perturbations, from a model-independent point of view, by
parametrizing the features directly with modified "slow-roll" parameters. We
can obtain a self-consistent power-spectrum, together with enhanced
non-Gaussianity, which grows with a quantity that parametrizes the
sharpness of the step. With this treatment it is straightforward to generalize
and include features in other coefficients of the effective action of the
inflaton field fluctuations. Our conclusion in this case is that, excluding
extrinsic curvature terms, the only interesting effects at the level of the
bispectrum could arise from features in the first slow-roll parameter
or in the speed of sound . Finally, we derive an upper bound on
the parameter from the consistency of the perturbative expansion of the
action for inflaton perturbations. This constraint can be used for an
estimation of the signal-to-noise ratio, to show that the observable which is
most sensitive to features is the power-spectrum. This conclusion would change
if we consider the contemporary presence of a feature and a speed of sound , as, in such a case, contributions from an oscillating folded
configuration can potentially make the bispectrum the leading observable for
feature models.Comment: 31 pages, 11 figures; references added, accepted version for
publication in JCA
Almost sure existence of global weak solutions for super-critical Navier-Stokes equations
In this paper we show that after suitable data randomization there exists a
large set of super-critical periodic initial data, in for some , for both 2d and 3d Navier-Stokes equations for
which global energy bounds are proved. As a consequence, we obtain almost sure
super-critical global weak solutions. We also show that in 2d these global weak
solutions are unique.Comment: 22 pages, a revised argument in Section 5, the cas
Perturbative Unitarity of Inflationary Models with Features
We consider the pertubative consistency of inflationary models with features
with effective field theory methods. By estimating the size of one-loop
contributions to the three-point function, we find the energy scale where their
contribution is of the same order of the tree-level amplitude. It is well-known
that beyond that scale, perturbative unitarity is lost and the theory is no
more under theoretical control. Requiring that all the relevant energy scales
of the problem are below this cutoff, we derive a strong upper bound on the
sharpness of the feature, or equivalently on its characteristic time scale,
which is independent on the amplitude of the feature itself. We point out that
the sharp features which seem to provide better fits to the CMB power spectrum
are already outside this bound, questioning the consistency of the models that
predict them
Generalised tensor fluctuations and inflation
Using an effective field theory approach to inflation, we examine novel
properties of the spectrum of inflationary tensor fluctuations, that arise when
breaking some of the symmetries or requirements usually imposed on the dynamics
of perturbations. During single-clock inflation, time-reparameterization
invariance is broken by a time-dependent cosmological background. In order to
explore more general scenarios, we consider the possibility that spatial
diffeomorphism invariance is also broken by effective mass terms or by
derivative operators for the metric fluctuations in the Lagrangian. We
investigate the cosmological consequences of the breaking of spatial
diffeomorphisms, focussing on operators that affect the power spectrum of
fluctuations. We identify the operators for tensor fluctuations that can
provide a blue spectrum without violating the null energy condition, and
operators for scalar fluctuations that lead to non-conservation of the comoving
curvature perturbation on superhorizon scales even in single-clock inflation.
In the last part of our work, we also examine the consequences of operators
containing more than two spatial derivatives, discussing how they affect the
sound speed of tensor fluctuations, and showing that they can mimic some of the
interesting effects of symmetry breaking operators, even in scenarios that
preserve spatial diffeomorphism invariance.Comment: 20 pages. V3: typos corrected and references added. Matches version
published in JCA
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